Dashpots with amplitude-dependent shock absorption like the above have been developed for use with motor vehicle wheels in particular, to ensure that the level of shock absorption will decrease when the oscillations are both high in frequency and narrow in amplitude. A dashpot of this genus is known from EP 1 152 166 A1. The device features a hydraulically parallel cylindrical pressure-compensation chamber partitioned into two halves by an axially displaceable floating piston. At least one face of the floating piston is provided with a resilient bumper. The bumper is in the form of an O ring that fits into a groove. This is a drawback in that the bumper's performance curve is so hard that the floating piston's impact against the bottom of the pressure-compensation chamber will lead to jolts that are at least heard and in the worst case even felt inside the vehicle. The sudden impacts on the bumper also soon lead to wear. Furthermore, a hard bumper accelerates the transition between soft and hard dashpot-performance curves. This situation in turn can result in impermissibly steep acceleration of the piston rod at the transition point, perceived inside the vehicle as irritating noise or dissonant shock absorption.